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Additional resources for Stretching and Shrinking: Understanding Similarity (Connected Mathematics 2, Grade 7)
You can change the size and shape of the image by grabbing and dragging the buttons. qxd 5/18/06 3:12 PM Page 59 Here are examples of the image after it has been resized. 1 • How do you think this technique produced these variations of the original shape? • Which of these images appears to be similar to the original? Why? One way to describe and compare shapes is by using ratios. A ratio is a comparison of two quantities such as two lengths. The original figure is about 10 centimeters tall and 8 centimeters wide.
When you find the area of a square, you multiply the length of the side by itself. For a square with a side length of 3 units, you multiply 3 3 3 (or 32 ) to get 9 square units. For this reason, you call 9 the square of 3. Three is called the square root of 9. The symbol, “ ! ” is used for the square root. This gives the fact family below. 9 = 3 38. The square has an area of 10 square units. Write the side length of this square using the square root symbol. 39. Multiple Choice What is the square root of 144?
2. What types of rules produced figures similar to Mug Wump? Explain. 3. What types of rules produced figures that were not similar to Mug Wump? Explain. 4. When a figure is transformed to make a similar figure, some features change and some stay the same. What does the scale factor tell you about how the figure changes? qxd 5/18/06 3:07 PM Page 38 ! Similar Polygons In Shapes and Designs, you learned that some polygons can fit together to cover, or tile, a flat surface. For example, the surface of a honeycomb is covered with a pattern of regular hexagons.